It is it actually a published procedure on your type to leave the gear down to cool the brakes, or just something someone thought of?
If we depart and leave the gear down on the 777, we have specific performance data for that configuration.
If it's actually a certified procedure on your aircraft, the performance data should also be published.
It would not be safe to simply decided to raise the gear in response to an engine failure, as you would have already lost performance, and gear retraction is often a high drag sequence.